Sampling
I was given a list of all of the students at North Olmsted High School which was accessible with Minitab. Using the Minitab random number generator, I randomly selected 150 students from the entire student body at NOHS, my population of interest (Command: Calc; Random Data; Sample from columns). I then put my results, or student names, into alphabetical order so that it was easier for me to find how to contact them (Command: Manip; Sort). After I obtained a list of all of the names, I printed 150 copies of my survey. I went to the Guidance office and found each individual’s first period class, teacher, and room number. I placed each student’s name, period of availability, teacher, and room number on sticky notes and sent them to the office for distribution. If a student was discovered to go to Polaris, band, or gym first period, I used a different period and sent it to that teacher. If a student went to Polaris full time or did not visit the school building at all during the day, then I was not able to contact them; therefore, they contributed to the response bias. The participation survey that students were asked to complete looked like this:
________________________________________________________________________
BJ
For each of the following questions, check the box of the statement that best describes you.
How would you rate your participation in English class?
___ I never participate
___ I rarely participate
___ I participate sometimes
___ I participate most of the time
___ I always participate
How would you rate your participation in Math class?
___ I never participate
___ I rarely participate
___ I participate sometimes
___ I participate most of the time
___ I always participate
Chi-squared test for homogeneity
Ho: the true proportions Amath, Bmath, Cmath, Dmath, and Emath are equal to Aenglish, Benglish, Cenglish, Denglish, and Eenglish, respectively
Ha: the true proportions Amath, Bmath, Cmath, Dmath, and Emath are not equal to Aenglish, Benglish, Cenglish, Denglish, and Eenglish, respectively
Alpha: 0.05
Observed Values:
|
CLASS |
NeverParticipate |
RarelyParticipate |
ParticipateSometimes |
ParticipateMostOfTheTime |
AlwaysParticipate |
|
|
English |
5 |
11 |
28 |
39 |
23 |
|
|
math |
10 |
15 |
34 |
31 |
16 |
|
Corresponding Expected Values:
|
Expected Values Matrix |
|
|
|
|
|
7.5 |
13 |
31 |
35 |
19.5 |
|
7.5 |
13 |
31 |
35 |
19.5 |
All values are greater than five - x² test will uphold
df = 4
x² = 5.033392414
p-value = .2838883546
We fail to reject the null hypothesis at any reasonable level of significance because our p-value is greater than alpha. Therefore, there is insufficient evidence to conclude that the true proportions Amath, Bmath, Cmath, Dmath, and Emath are equal to Aenglish, Benglish, Cenglish, Denglish, and Eenglish, respectively.
